About This PhD Project

Project Description

TMCS is an EPSRC Centre for Doctoral Training operated by the Universities of Oxford, Bristol and Southampton. In year one you will be based in Oxford with a cohort of around 12–15 other TMCS students, and will receive in-depth training in fundamental theory, software development, and chemical applications, delivered by academics from all three Universities. Successful completion of the year-one program leads to the award of an Oxford MSc, and progression to the 3-year PhD project based in Southampton, and detailed below.

Developing the next generation of large-scale quantum chemistry simulations The accurate description of the electrons which play a crucial role in the bonding of atoms into molecules, surfaces and solids, requires solving the equations of quantum mechanics. Using only fundamental physical constants as known quantities, these equations are so general and powerful that any observable property of matter can be extracted from their solution. The solution of these equations for real materials without any empirical input is computationally very demanding and a number of computational “first principles” methods have been developed for this purpose. The Density Functional Theory (DFT) formulation of quantum mechanics stands out from all first principles methods as it allows one to make useful approximations for the very complicated components of electronic motion called exchange and correlation.

Conventional DFT calculations are limited to a few hundred atoms at most as the computational effort increases with the third power of the number of atoms. To overcome this limitation we have developed a reformulation of DFT with computational cost that increases only linearly with the number of atoms, which allows calculations with thousands of atoms. Our linear-scaling DFT theory is implemented in the ONETEP program which has been designed to achieve large basis set accuracy and run on parallel supercomputers. Localised orbitals are optimised in situ, and linear-scaling is achieved by taking advantage of the exponential decay of the density matrix according to the physical principle of “near-sightedness of electronic matter” of Nobel Prize winner Walter Kohn. Being able to do such large-scale quantum calculations is one thing but using them to solve real problems of industrial relevance is another which throws up other challenges to be overcome. The point is that molecules, biomolecules and nanoparticles are not isolated and not at a temperature of zero Kelvin. On the contrary, they interact heavily with each other and their environment (e.g. solvent) and are in constant thermal motion.

Therefore, this PhD will be focused towards developing new models with which to improve and augment our quantum simulations in order to achieve the required level of realism. For example, DFT is formally an exact theory but in practice, the accuracy it can achieve is limited by the approximation of the so-called exchange-correlation (XC) functional. Amongst the most accurate approximations are the range-separated hybrid functionals which include Hartree-Fock exchange via distance-modified a Coulomb operator. Most importantly, these functionals do not only provide accurate ground state properties but also excited-state properties making them suitable for important technological applications. The capability for range-separated hybrid XC functionals will be developed within the linear-scaling framework of the ONETEP code by developing a non-orthogonal generalised Wannier function two-electron integral “engine” that it is able to treat modified Coulomb operators. Several types of range-separated XC functionals will be implemented and validated in calculations of ground and excited state properties. Further goals of this project involve developing and implementing novel DFT theories which connect with wavefunction-based methods as well as introducing multi-scale models such as solvent models and polarisable force fields which are necessary for a realistic description of the environment of the quantum system. These developments will allow simulations with unprecedented large numbers of atoms and realism, and will open the way for new applications such as the simulation of biomolecular association (drug design) or organic photovoltaic materials.